On encounter rates in star clusters

Abstract

Close encounters between stars in star forming regions are important as they can perturb or destroy protoplanetary discs, young planetary systems, and stellar multiple systems. We simulate simple, viralised, equal-mass $N$-body star clusters and find that both the rate and total number of encounters between stars varies by factors of several in statistically identical clusters due to the stochastic/chaotic details of orbits and stellar dynamics. Encounters tend to rapidly `saturate' in the core of a cluster, with stars there each having many encounters, while more distant stars have none. However, we find that the fraction of stars that have had at least one encounter within a particular distance grows in the same way (scaling with crossing time and half-mass radius) in all clusters, and we present a new (empirical) way of estimating the fraction of stars that have had at least one encounter at a particular distance.